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That is why our hypotheses always refer to the population, and never to the
sample of people, plants, animals, or events in our study .
You will recall from Chap. 1 that we used the symbol: X to refer to the mean of
the sample we use in our research study (See Sect. 1.1 ) .
We will use the symbol: l (the Greek letter ‘‘mu’’) to refer to the population
mean.
In testing our hypotheses, we are trying to decide which one of two competing
hypotheses about the population mean we should accept given our data set.
3.2.2 The Null Hypothesis and the Research (Alternative)
Hypothesis
These two hypotheses are called the null hypothesis and the research hypothesis.
Statistics textbooks typically refer to the null hypothesis with the notation: H 0 .
The research hypothesis is typically referred to with the notation: H 1 , and it is
sometimes called the alternative hypothesis.
Let’s explain ﬁrst what is meant by the null hypothesis and the research
hypothesis:
(1) The null hypothesis is what we accept as true unless we have compelling
evidence that it is not true.
(2) The research hypothesis is what we accept as true whenever we reject the null
hypothesis as true.
This is similar to our legal system in America where we assume that a supposed
criminal is innocent until he or she is proven guilty in the eyes of a jury. Our null
hypothesis is that this defendant is innocent, while the research hypothesis is that
he or she is guilty.
In the great state of Missouri, every license plate has the state slogan: ‘‘Show
me.’’ This means that people in Missouri think of themselves as not gullible
enough to accept everything that someone says as true unless that person’s actions
indicate the truth of his or her claim. In other words, people in Missouri believe
strongly that a person’s actions speak much louder than that person’s words.
Since both the null hypothesis and the research hypothesis cannot both be true,
the task of hypothesis testing using statistical formulas is to decide which one you
will accept as true, and which one you will reject as true.
Sometimes in science research a series of rating scales is used to measure
people’s attitudes toward a company, toward one of its products, or toward their
intention-to-buy that company’s products. These rating scales are typically 5-, 7-,
or 10-point scales, although other scale values are often used as well.
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